# A small remote village receives radio broadcasts from two radio stations, a news station and a music station. Of the listeners who are tuned to the news station, 70% will remain listening to the news after the station break that occurs each half hour, while 30% will switch to the music station at the station break. Of the listeners who are tuned to the music station, 60% will switch to the news station at the station break, while 40% will remain listening to the music. Suppose everyone is listening to the news at 8:15 A.M. a. Give the stochastic matrix that describes how the radio listeners tend to change stations at each station break. Label the rows and columns. b. Give the initial state vector c. What percentage of the listeners will be listening to the music station at 9:25 A.M. (after the station breaks at 8:30 and 9:00 A.M.)?

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A small remote village receives radio broadcasts from two radio stations, a news station and a music station. Of the listeners who are tuned to the news station, 70% will remain listening to the news after the station break that occurs each half hour, while 30% will switch to the music station at the station break. Of the listeners who are tuned to the music station, 60% will switch to the news station at the station break, while 40% will remain listening to the music. Suppose everyone is listening to the news at 8:15 A.M. a. Give the stochastic matrix that describes how the radio listeners tend to change stations at each station break. Label the rows and columns. b. Give the initial state vector c. What percentage of the listeners will be listening to the music station at 9:25 A.M. (after the station breaks at 8:30 and 9:00 A.M.)?

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Step 1

Given:

Of the listeners, 70% will remain listening to the news after the station break that occurs each half hour, while 30% will switch to the music station at the station break. where 30% will switch to the music station at the station break. Of the listeners who are tuned to the music station, 60% will switch to the news station at the station break, while 40% will remain listening to the music. And also, it is supposed that everyone is listening to the news at 8:15 A.M.

Step 2

Now for stochastic matrix:

A stochastic matrix is a square matrix whose columns are probability vectors.

Hence in this case:

Step 3

Now for initial vector:

Since from the given information everyone started listening news at ...

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